微孔线弹性材料的守恒律和完备性定理

本文用无穷小变换群使作用量不变的思想证明了广义Noether定理,且得到一类守恒律,对线性均匀微孔弹性材料阐明了尺度变换下守恒律的可能性,且给出了完备性定理的证明。     

Axisymmetric boundary-value problems in a piezoelectric medium

Based on the general solution of three-dimensional problems in piezoelectric medium, with the method of Green's functins^[2], axisymmetric boundary-value problems are discussed. The purpose of this research is for analyzing the effective on mechanics and electricity of the piezoelectric ceramics caused by voids and inclusions. The displacement, traction and electric Green's functions corresponding to circular ring loads acting in the interior of a piezoelectric ceramic are obtained. A cylindrical coordinate system is employed and Hankel transform are applied with respect to radial coordinates. Explicit solutions for Green's functions are presented in terms of infinite integrals of Lipshitz-Hankel type. By solving a traction boundary-value problem, the solution scheme is illustrated. Supported by the National Natural Science Foundation of China and the Foundation of the Open Laboratory of Solid Mechanics.     

The structure of the compound Cd3P2

Structure of Cd₃P₂ (P4₂/nmc, a = b = 8.7390 Å, c = 12.2523 Å) has been solved and refined up to R = 3.78% using precision X-ray diffraction experimental data (λ-MoK _α, graphite monochromator on a primary beam, 11529 reflections). Interatomic distances and valence angles are determined. Phosphorus forms a face-centered cubic lattice in which 3/4 tetrahedral voids are occupied by cadmium atoms in the crystal structure. The structure can be described by two equivalent models in which the positions of cadmium atoms, which occupy tetrahedral voids following the “diamond principle,” are preserved, while the remaining free and occupied voids change their places.     

A Novel Three‐Dimensional Copper(II) 1,2‐Ethylenediphosphonate Framework with Channel‐like Voids

Turquoise monoclinic single crystals of the novel three‐dimensional Cu₂[μ₈‐O₃P(CH₂)₂PO₃] · 3.2H₂O coordination polymer were prepared using the silica gel method. Space group C2/m (no. 12) with a = 1483.6(2), b = 668.44(8), c = 436.30(6) pm, β = 93.28(2)°. The Cu²⁺ cation is coordinated by four oxygen atoms stemming from the 1,2‐ethylenediphosphonate dianions in a square planar manner and two water molecules in the axial positions. The connection between the Cu²⁺ cations and the [CPO₃] units from the 1,2‐ethylenediphosphonate dianions leads to layers parallel to (100), which are linked by the ethylene groups to a three‐dimensional framework with channel‐like voids. The channel‐like voids accommodate water molecules not bound to Cu²⁺ and extend parallel to [001] with an opening of about 550 pm × 260 pm. Magnetic measurements reveal an antiferromagnetic behavior due to a superexchange coupling between Cu²⁺ ions through an oxygen bridge. The UV/Vis spectrum reveals three d–d transition bands at 694, 774, and 918 nm. The compound can be fully dehydrated by thermal treatment and rehydrated by storage in ambient air.     

Experimental Cosserat elasticity in open-cell polymer foam

Reticulated open-cell polymer foams exhibit substantial size effects in torsion and bending: slender specimens are more rigid than anticipated via classical elasticity. Such size effects are predicted by Cosserat (micropolar) elasticity, which allows points to rotate as well as translate and incorporates distributed moments (couple stresses). The Cosserat characteristic length is larger than the cell size. The Cosserat coupling coefficient is larger than in dense closed-cell foams and approaches 1 for foam with 0.4 mm cells.     

Dimensionality effects in void-induced explosive sensitivity

The dimensionality of defects in high explosives controls their heat generation and the expansion of deflagrations from them. We compare the behaviour of spherical voids in three dimensions to that of circular voids in two dimensions. The behaviour is qualitatively similar, but the additional focusing along the extra transverse dimension significantly reduces the piston velocity needed to initiate reactions. However, the reactions do not grow as well in three dimensions, so detonations require larger piston velocities. Pressure exponents are seen to be similar to those for the two-dimensional system.     

Elastic–plastic ductile damage model based on strain-rate plastic potential

Modeling of ductile damage is generally done using analytical potentials, which are expressed in the stress space. In this paper, for the first time it is shown that strain-rate potentials which are exact conjugate of the stress-based potentials can be instead used to model the dilatational response of porous polycrystals. A new integration algorithm is also developed. It is to be noted that a strain-rate based formulation is most appropriate when the plastic flow of the matrix is described by a criterion that involves dependence on all stress invariants. In such cases, although a strain-rate potential is known, the stress-based potential cannot be obtained explicitly. While the proposed framework based on strain-rate potentials is general, for comparison purposes in this work we present an illustration of the approach for the case of a porous solid with von Mises matrix containing randomly distributed spherical cavities. Comparison between simulations using the strain-rate based approach and the classical stress-based Gurson's criterion in uniaxial tension is presented. These results show that the model based on a strain-rate potential predicts the dilatational response with the same level of accuracy.     

Measurements of hall-effect and sheet resistivity as a function of temperature on hot,phosphorous implants in silicon

Abstract

Results of Hall-effect measurements as a function of temperature on a layer formed by hot, phosphorous (P³¹) implant in Si at 400 keV energy in a random direction are presented; the dose used was 10¹⁵ ions cm^?2. The electrical behaviour of the layer as a function of isochronal annealing was examined.

A detailed analysis of the measured quantities n _8eff, the effective surface density of free carriers, and μ_eff, the effective mobility, down to 4.2°K is presented using the integral equations:

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These formulae were solved numerically, the input data viz: the distribution of donor centres and compensating damage centres being assumed from the current literature.

Results from this analysis indicate a rather complicated distribution of current flow in the layer as a function of temperature, indicating that the traditional interpretation of Hall measurements based on a homogeneous distribution model is of questionable validity.     

Investigation on dislocation-based mechanisms of void growth and coalescence in single crystal and nanotwinned nickels by molecular dynamics simulation

Abstract

Molecular dynamics simulations were conducted to elucidate dislocation mechanisms of the void growth and coalescence in single crystal and nanotwinned nickels subjected to uniaxial tension. The simulation results reveal that twin boundary is capable of decreasing the critical stress, suppressing the emission of dislocations and reducing the overall stiffness of the crystal. A size-scale dependence of critical stress is definitely illustrated through stress–strain response, where the larger void size leads to the lower critical stress and strain. It is the successive emissions of leading partials and the subsequent trailing partials that cause the atoms on the void surfaces to escape from the void surfaces continually, and consequently the voids grow to be larger and larger with increasing strain. The voids in the nanotwinned nickel coalesce earlier than those in the single crystal nickel even though the initiation of dislocations in the former is later than that in the latter. Void fraction remains a constant during elastic deformation, while it presents a linear increase with increasing strain during plastic deformation. Evolution of void fraction during void growth and coalescence is independent on void size.     

微孔压电弹性动力学的能量原理

根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出一条简单而统一的新途径,系统地建立了微孔压电弹性动力学的能量原理,给出一个重要的以卷积表示的积分关系式,可以认为,在力学上它是广义虚功原理的表式,从该式出发,不仅能得到微孔压电弹性动力学的虚功原理和互等定理,而且通过作者所给出的一系列广义Legendre变换,能系统地导出成互补关系的11类变量、9类变量、6类变量和3类变量简化Gurtin型变分原理的泛函,同时,通过这条新途径,还能清楚地阐明这些原理之间的内在联系。